then necessarily \(\zeta =\mu ^A\) . Actually, this characteristic property of the inner balayage \(\mu ^A\)  needs only to be verified for certain countably many \(\nu _j\in \mathcal {E}^+_\alpha \)  that are independent of the choice of \(\mu \in \mathfrak {M}^+\) .This result has recently been extended to inner balayage on a locally compact space, see [1]}. This fact is implied by the observation that there exist countably many \(\nu _j\in \mathcal {E}^+_\alpha \)  whose potentials \(\kappa _\alpha \nu _j\)  form a dense subset of \(C_0(\mathbb {R}^n)\) , see [2]}.

